There have been proposed various methods for polymerizing an .alpha.-olefin having 3 or more carbon atoms by using a catalyst composed of a solid catalytic ingredient in which a titanium tetrahalide is carried on a magnesium compound, and an organic aluminum compound, to increase the yield of the resultant polymer per unit weight of the solid catalytic ingredient to such an extent that an operation for removing the used catalyst from the resultant polymer can be omitted.
For example, Japanese Patent Application Laid-open No. 54-107987 discloses a method for polymerizing an .alpha.-olefin using a catalyst composed of a solid catalytic component which has been prepared by reacting aluminum chloride with a reaction product by hydropolysiloxane and a Grignard compound, and by bringing the resultant solid product into contact with a titanium tetrahalide in the presence of an organic acid ester, and of a trialkyl aluminum. By this method, the resultant polymer yield per unit weight of the catalyst can be remarkably increased as compared with a method in which a titanium trichloride-organic aluminum catalyst is employed for polymerization of an .alpha.-olefin, but according to the example of the above-cited Laid-open specification, the polymer yield per g of the solid catalytic component per hour of polymerization time remains as low as 3,000 g or less. To permit omission of an operation for removing the residual catalyst from the resultant polymer, it is desired that the polymer yield be further increased.